In this work, we investigate the global transport properties and the destruction of invariant structures in the extended nontwist standard map. We propose a robust methodology based on the statistics of Poincaré recurrences and Slater's theorem to identify the most resilient transport barrier in the phase space: the shearless curve. By detecting quasi-periodic trajectories characterized by exactly three distinct recurrence times, we accurately determine the critical perturbation parameter c_r associated with the global transition to chaos. To validate our approach, we introduce a geometric similarity measure based on the Hausdorff distance, demonstrating that the boundary curve identified via Slater's theorem strictly coincides with the theoretical shearless curve obtained via the standard indicator-point method. A major advantage of this recurrence-based framework is its complete independence from spatial symmetries, enabling the precise identification of transport barriers in both symmetric (odd m) and non-symmetric (even m) perturbation regimes. Furthermore, we systematically map the (a,b) parameter space to construct detailed robustness diagrams, delineating regimes where invariant curves persist from fully chaotic, barrier-less domains. Our results establish recurrence-time statistics as a highly effective and universal diagnostic tool for studying transport barriers in nontwist Hamiltonian systems.